| Let f be a rational map defined on the Riemann sphere. Then f defines a dynamical system whose chaotic locus is called the Julia set. A pinching deformation, ft, t > 0, is a one-parameter family of deformations of f. It is a way to create a parabolic cycle by forcing an attracting cycle and a repelling cycle to collide. The main result shows that for certain pinching deformations, if ft → g uniformly, then the Julia set of ft converges in the Hausdorff topology to the Julia set of g in the Hausdorff topology. |
